send POST method should use the iRules sideband method. The difficulty is whether your server POST does not require username, password or Token authentication about F5?

firstly, F5 whether can ping NGFW and telnet NGFW 80(assume NGFW api service port is 80)?

secondly, if F5 can not telnet NGFW 80,  F5 need to add network route to NGFW, make sure F5 can telnet NGFW 80

here is the code, NGFW(example NGFW ip is 10.0.0.10, api service port is 80) with no authentication for POST 

when ASM_REQUEST_DONE priority 500 {
    set asm_ip [ASM::client_ip]
    set asm_json "\{\"Client_address\":$asm_ip\}"
    set content_length [string length $asm_json]
    set data "POST /sample/post/json HTTP/1.0\r\nHost: test.com\r\nContent-type: application/json\r\nContent-Length: ${content_length}\r\n\r\n${asm_json}"
    if { [catch {connect -time 1000 -idle 30 -status conn_status 10.0.0.10:80} conn_id] == 0 && $conn_id ne "" } {
        log local0. "Connect returns: $conn_id and conn status: $conn_status"
        set send_bytes [send -timeout 1000 -status send_status $conn_id $data]
        log local0. "Sent $send_bytes with status $send_status"
        close $conn_id
        return
    } else {
        log local0. "Connection could not be established to NGFW"
    }
}